In the first row is the graph of the unit pulse function and its Fourier transform , a function of frequency . Translation (that is, delay) in the time domain goes over to complex phase shifts in the frequency domain. In the second row is shown , a delayed unit pulse, beside the real and imaginary parts of the Fourier transform. The Fourier transform decomposes a function into eigenfunctions for the group of translations.
Champeney, D.C. (1987), A Handbook of Fourier Theorems, Cambridge University Press
de Groot, Sybren R.; Mazur, Peter (1984), Non-Equilibrium Thermodynamics (2nd ed.), New York: Dover
Marín Antuña, José (1990), Teoría de funciones de variable compleja (2nd ed.), Havana: Editorial Pueblo y Educación
Chatfield, Chris (2004), The Analysis of Time Series: An Introduction, Texts in Statistical Science (6th ed.), London: Chapman & Hall/CRC
Feller, William (1971), An Introduction to Probability Theory and Its Applications. Vol. II. (Second ed.), New York: John Wiley & Sons.
Wiener, Norbert (1949), Extrapolation, Interpolation, and Smoothing of Stationary Time Series With Engineering Applications, Cambridge, Mass.: Technology Press and John Wiley & Sons and Chapman & Hall
Kirillov, Alexandre; Gvichiani, Alexei (1982), Théorèmes et problèmes d'analyse fonctionnelle, Djilali Embarek, translator, Moscow: Mir
Kolmogórov, Andréi Nikolaevich; Fomín, Serguei Vasílievich (1978), Elementos de la teoría de funciones y del análisis functional, Carlos Vega, translator (3rd ed.), Moscow: Mir
Guelfand, Israel Moiseevich; Vilenkin, N.Y. (1967), Les distributions tome 4: applications de l'analyse harmonique, G. Rideau, translator, Paris: Dunod
Widder, David Vernon; Wiener, Norbert (August 1938), "Remarks on the Classical Inversion Formula for the Laplace Integral", Bulletin of the American Mathematical Society44: 573–575, doi:10.1090/s0002-9904-1938-06812-7
Clozel, Laurent; Delorme, Patrice (1985), "Sur le théorème de Paley-Wiener invariant pour les groupes de Lie réductifs réels", C. R. Acad. Sci. Paris, série I300: 331–333
Paley, R.E.A.C.; Wiener, Norbert (1934), Fourier Transforms in the Complex Domain, American Mathematical Society Colloquium Publications, Providence, Rhode Island: American Mathematical Society
Grafakos, Loukas (2004), Classical and Modern Fourier Analysis, Prentice-Hall, ISBN 0-13-035399-X.
Grafakos, Loukas; Teschl, Gerald (2013), "On Fourier transforms of radial functions and distributions", J. Fourier Anal. Appl.19: 167–179, doi:10.1007/s00041-012-9242-5.
Hewitt, Edwin; Ross, Kenneth A. (1970), Abstract harmonic analysis. Vol. II: Structure and analysis for compact groups. Analysis on locally compact Abelian groups, Die Grundlehren der mathematischen Wissenschaften, Band 152, Berlin, New York: Springer-Verlag.
Titchmarsh, E (1948), Introduction to the theory of Fourier integrals (2nd ed.), Oxford University: Clarendon Press (published 1986), ISBN 978-0-8284-0324-5.
Vretblad, Anders (2000), Fourier Analysis and its Applications, Graduate Texts in Mathematics, 223, New York: Springer Publishing, ISBN 0-387-00836-5
Wilson, R. G. (1995), Fourier Series and Optical Transform Techniques in Contemporary Optics, New York: Wiley, ISBN 0-471-30357-7.
